Author： Huang W-T.
Publisher： Springer Publishing Company
ISSN： 0020-3157
Source： Annals of the Institute of Statistical Mathematics, Vol.51, Iss.2, 1999-06, pp. : 281-299
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Abstract
Consider k (k ≥ 2) populations whose mean _i and variance _i^2 are all unknown. For given control values _0 and _0^2, we are interested in selecting some population whose mean is the largest in the qualified subset in which each mean is larger than or equal to _0 and whose variance is less than or equal to _0^2. In this paper we focus on the normal populations in details. However, the analogous method can be applied for the cases other than normal in some situations. A Bayes approach is set up and an empirical Bayes procedure is proposed which has been shown to be asymptotically optimal with convergence rate of order O(ln^2 n/n). A simulation study is carried out for the performance of the proposed procedure and it is found satisfactory.
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